Legendre Pseudospectral Method based Optimal Control of Water-Borne Disease Transmission

Pathogen suppressing and immune boosting drugs, are used as control measure for regulating the infections due to water borne disease. A mathematical SIWR (susceptible-infectious-recovered) model is considered in which the $W$ compartment tracks the concentration of pathogen in water. An optimal scheme for disease control is proposed in this paper by converting the original optimal control problem to a nonlinear programming problem (NLP). This transformation is done by Legendre pseudospectral method (LPSM) and the resulting NLP problem is solved. The objective of minimizing the count of infected population, along with drug dosage cost is addressed. The simulation results reported illustrates the effectiveness of the proposed optimal drug use strategy.